Finite Group Databasebeta

← #11634186

Subgroups — #11634186

Order 768.

2238 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5543C211yesmaximal, characteristic, complemented
2C2×#5470C211yesmaximal, characteristic, complemented
3C3×C4×#121C211yesmaximal, characteristic
4#82637C212yesmaximal
5#82379C211yesmaximal, characteristic, complemented
6#82379C212yesmaximal, complemented
7#82353C212yesmaximal, complemented
8C4×#924C211yesmaximal, characteristic, complemented
9#76324C212yesmaximal, complemented
10#76065C212yesmaximal, complemented
11#75498C214yesmaximal, complemented
12#74830C214yesmaximal, complemented
13#73900C212yesmaximal, complemented
14#73711C211yesmaximal, characteristic, complemented
15#73656C211yesmaximal, characteristic, complemented
16#73488C212yesmaximal, complemented
17#73465C212yesmaximal, complemented
18#59052—31nomaximal, Sylow
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×C4×D4C2212yes—
22C22×C3×C42C2211yescharacteristic
23C2×D4×Dic3C2212yes—
24C2×#926C2212yes—
25C22×C4⋊Dic3C2212yes—
26C2×#924C2212yes—
27C2×#924C2212yes—
28C2×#924C2211yescharacteristic
29C2×#924C2212yes—
30C2×#924C2212yes—
31C2×#924C2212yes—
32#5543—28no—
33C2×#890C2212yes—
34C2×#878C2214yes—
35#5470—28no—
36C2×#870C2212yes—
37C2×#869C2211yescharacteristic
38C2×#869C2212yes—
39C2×#869C2211yescharacteristic
40C2×C4×Dic6C2211yescharacteristic
41C2×C4×Dic6C2212yes—
42C2×C4×Dic6C2212yes—
43C3×#390C2211yescharacteristic
44C3×#389C2211yescharacteristic
45C3×#388C2212yes—
46C3×#386C2212yes—
47C3×#380C2211yescharacteristic
48C3×C4×C4⋊C4C2211yescharacteristic
49C3×C4×C22⋊C4C2212yes—
50#5221C2212yes—
51#5221C2214yes—
52#5220C2214yes—
53#5212C2211yescharacteristic
54#5210C2212yes—
55C4×#217C2212yes—
56#4984C2212yes—
57#4984C2212yes—
58#4982C2214yes—
59#4975C2212yes—
60#4975C2214yes—
61Dic3×C4⋊C4C2212yes—
62#4972C2212yes—
63#4951C2214yes—
64#4949C2214yes—
65#4949C2214yes—
66#4949C2214yes—
67#4948C2214yes—
68#4948C2214yes—
69#4946C2214yes—
70#4942C2214yes—
71Dic3×C22⋊C4C2214yes—
72C4×C4⋊Dic3C2211yescharacteristic
73C4×C4⋊Dic3C2212yes—
74#4933C2212yes—
75C4×Dic3⋊C4C2212yes—
76#4929C2211yescharacteristic
77#4929C2212yes—
78#4928C2212yes—
79#4928C2211yescharacteristic
80#4661C2214yes—
81#4657C2214yes—
82#4655C2214yes—
83#4647C2214yes—
84#4647C2214yes—
85#4646C2214yes—
86C2×#554—31no—
87C2×#533—31no—
88#2732—34no—
89#2552—32no—
90#2546—31no—
91#2542—31no—
92#2542—32no—
93#2454—32no—
94#2441—32no—
95#2429—32no—
96#2423—34no—
97#2417—32no—
98#2369—31no—
99#2363—32no—
100#2360—32no—
101C4×C22⋊Q8—31no—
102C4×#121D311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2312yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2312yes—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×Dic3C2314yes—
110C22×Dic6C2312yes—
111C22×Dic6C2311yescharacteristic
112C22×Dic6C2312yes—
113C3×#121Q818yescomplemented
114C3×C4×D4—24no—
115C3×C4×D4—44no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C22⋊C4C2312yes—
121C2×C3×C22⋊C4C2312yes—
122C2×C3×C22⋊C4C2312yes—
123C2×C3×C22⋊C4C2312yes—
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C42—24no—
126C2×C3×C42C2312yes—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×#217C2314yes—
132C2×#217C2314yes—
133C2×#217C2314yes—
134C2×#217C2312yes—
135C2×#217C2314yes—
136C2×#217C2312yes—
137D4×Dic3—28no—
138#926—28no—
139C2×C4⋊Dic3—28no—
140C2×C4⋊Dic3C2314yes—
141C2×C4⋊Dic3C2312yes—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2312yes—
145C2×C4⋊Dic3C2314yes—
146C2×C4⋊Dic3C2314yes—
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2311yescharacteristic
150#924—28no—
151#924—28no—
152#924—28no—
153#924—24no—
154#924—28no—
155#924—44no—
156C2×Dic3⋊C4C2314yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2314yes—
165C2×C4×Dic3C2314yes—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2314yes—
169#890—28no—
170#878—216no—
171#870—28no—
172#869—24no—
173#869—44no—
174#869D418yescomplemented
175C4×Dic6—28no—
176C4×Dic6—24no—
177C4×Dic6—28no—
178C3×#95C2312yes—
179C3×#95C2312yes—
180C3×#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190#554—68no—
191#533—68no—
192C2×C4⋊Q8—31no—
193C2×C4⋊Q8—31no—
194C2×C4⋊Q8—32no—
195C2×#125—32no—
196C2×#125—32no—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—31no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—34no—
204C2×#121C2×D311yescharacteristic
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×Q8—31no—
208C2×C4×D4—32no—
209C2×C4×D4C2×D311yescharacteristic
210C2×C4×D4C2×D312yes—
211C2×#117—32no—
212C22×C4⋊C4—32no—
213C22×C42C2×D311yescharacteristic
214#399—34no—
215#399—34no—
216#399—34no—
217#398—34no—
218#398—34no—
219#398—34no—
220#396—34no—
221#396—34no—
222#391—32no—
223#391—31no—
224#391—34no—
225#390—32no—
226#390—34no—
227#390C2×D311yescharacteristic
228#389—32no—
229#389—32no—
230#389—32no—
231#389—31no—
232#389—32no—
233#389—34no—
234#389—34no—
235#389C2×D311yescharacteristic
236#388—34no—
237#388C2×D312yes—
238#387—32no—
239#387—34no—
240#386—34no—
241#386C2×D312yes—
242#385—32no—
243#385—34no—
244#384—34no—
245#384—32no—
246#380—31no—
247#380—34no—
248#380C2×D311yescharacteristic
249C4×C4⋊C4—32no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4—32no—
255C4×C22⋊C4—34no—
256C4×C22⋊C4C2×D312yes—
257C24×C3C2411yescharacteristic
258C24×C3C2412yes—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4C2×Q814yes—
264C2×C3×D4C2×Q818yes—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—24no—
270C22×C3×C4—22no—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4—22no—
274C22×C3×C4—41no—
275C22×C3×C4—41no—
276C22×C3×C4C2×Q814yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2412yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2412yes—
284C22×C3×C4C2411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C22×Dic3—28no—
287C22×Dic3—44no—
288C22×Dic3—44no—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2414yes—
293C22×Dic3C2414yes—
294C22×Dic3C2412yes—
295C2×Dic6—24no—
296C2×Dic6—22no—
297C2×Dic6—24no—
298C2×Dic6—22no—
299C2×Dic6—22no—
300C2×Dic6—24no—
301C2×Dic6—42no—
302C2×Dic6—42no—
303C2×Dic6C2×D418yes—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—42no—
307C3×C4⋊C4C2×Q814yes—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4C2×Q818yes—
313C3×C42—22no—
314C3×C42—22no—
315C3×C42—22no—
316C3×C42—24no—
317C3×C42C2×D414yes—
318#217—28no—
319#217—28no—
320#217—28no—
321#217—24no—
322#217—44no—
323#217—42no—
324C4⋊Dic3—24no—
325C4⋊Dic3—22no—
326C4⋊Dic3—24no—
327C4⋊Dic3—22no—
328C4⋊Dic3—28no—
329C4⋊Dic3—44no—
330C4⋊Dic3—44no—
331C4⋊Dic3C2×D418yes—
332C4⋊Dic3C2×D418yes—
333C4⋊Dic3#4114yes—
334Dic3⋊C4—24no—
335Dic3⋊C4—28no—
336Dic3⋊C4—28no—
337Dic3⋊C4—28no—
338Dic3⋊C4—28no—
339Dic3⋊C4—24no—
340Dic3⋊C4—42no—
341Dic3⋊C4—44no—
342Dic3⋊C4—44no—
343C4×Dic3—24no—
344C4×Dic3—24no—
345C4×Dic3—28no—
346C4×Dic3—44no—
347C22×Q8—32no—
348C22×Q8—31no—
349C22×Q8—32no—
350C22×D4C22×D311yescharacteristic
351C22×D4C22×D312yes—
352C23×C4—34no—
353C23×C4C22×D312yes—
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C4⋊Q8—38no—
358C4⋊Q8—64no—
359C4⋊Q8—124no—
360#125—68no—
361#125—68no—
362C22⋊Q8—616no—
363C22⋊Q8—68no—
364C22⋊Q8—68no—
365C22⋊Q8—68no—
366C22⋊Q8—64no—
367C22⋊Q8—68no—
368C22⋊Q8—124no—
369#121Dic618yescomplemented
370C4×Q8—68no—
371C4×Q8—68no—
372C4×Q8—64no—
373C4×D4—24no—
374C4×D4—44no—
375C4×D4—68no—
376#117—68no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—32no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—68no—
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C4⋊C4C22×D312yes—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4C22×D312yes—
408C2×C22⋊C4C22×D312yes—
409C2×C22⋊C4C22×D312yes—
410C2×C22⋊C4C22×D312yes—
411C2×C22⋊C4C22×D312yes—
412C2×C42—24no—
413C2×C42—34no—
414C2×C42—32no—
415C2×C42—32no—
416C2×C42—34no—
417C2×C42C22×D312yes—
418C2×C42C22×D311yescharacteristic
419C2×C42C22×D311yescharacteristic
420C2×C42C22×D311yescharacteristic
421C2×C42C22×D311yescharacteristic
422#95—32no—
423#95—34no—
424#95—32no—
425#95—32no—
426#95—34no—
427#95—32no—
428#95—32no—
429#95—34no—
430#95—34no—
431#95C22×D312yes—
432#95C22×D312yes—
433#95C22×D312yes—
434C23×C3—21no—
435C23×C3—22no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—21no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—21no—
446C23×C3C22×Q814yes—
447C23×C3C22×Q812yes—
448C23×C3C2511yescharacteristic
449C3×D4—28no—
450C3×D4—48no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—28no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—44no—
471C2×C3×C4—44no—
472C2×C3×C4—48no—
473C2×C3×C4C22×D412yes—
474C2×C3×C4C22×D412yes—
475C2×C3×C4C22×D412yes—
476C2×C3×C4C22×Q812yes—
477C2×C3×C4C22×Q814yes—
478C2×C3×C4C22×Q812yes—
479C2×C3×C4C2×#4112yes—
480C2×C3×C4H(5,𝔽2)12yes—
481C2×C3×C42−1+412yes—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—24no—
486C2×Dic3—22no—
487C2×Dic3—24no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—24no—
491C2×Dic3—22no—
492C2×Dic3—24no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—88no—
499C2×Dic3C22×D418yes—
500C2×Dic3C2×#4114yes—
501Dic6—48no—
502Dic6—48no—
503Dic6—44no—
504C24C23×D311yescharacteristic
505C24C23×D312yes—
506C2×Q8—38no—
507C2×Q8—62no—
508C2×Q8—64no—
509C2×Q8—64no—
510C2×Q8—62no—
511C2×Q8—62no—
512C2×Q8—64no—
513C2×Q8—122no—
514C2×Q8—122no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4C2×Dic614yes—
520C2×D4C2×Dic618yes—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—32no—
531C22×C4—34no—
532C22×C4—32no—
533C22×C4—32no—
534C22×C4—32no—
535C22×C4—34no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—68no—
539C22×C4—124no—
540C22×C4—124no—
541C22×C4C2×Dic614yes—
542C22×C4C23×D312yes—
543C22×C4C23×D311yescharacteristic
544C22×C4C23×D311yescharacteristic
545C22×C4C23×D312yes—
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D312yes—
548C22×C4C23×D311yescharacteristic
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—38no—
554C4⋊C4—38no—
555C4⋊C4—34no—
556C4⋊C4—42no—
557C4⋊C4—68no—
558C4⋊C4—68no—
559C4⋊C4—68no—
560C4⋊C4—68no—
561C4⋊C4—64no—
562C4⋊C4—68no—
563C4⋊C4—62no—
564C4⋊C4—64no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—62no—
568C4⋊C4—124no—
569C4⋊C4—124no—
570C4⋊C4—124no—
571C4⋊C4—124no—
572C4⋊C4—122no—
573C4⋊C4C2×Dic614yes—
574C22⋊C4—24no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—68no—
579C22⋊C4—68no—
580C22⋊C4—64no—
581C22⋊C4—68no—
582C22⋊C4—124no—
583C22⋊C4—122no—
584C22⋊C4C2×Dic618yes—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—24no—
589C42—68no—
590C42—64no—
591C42—64no—
592C42—124no—
593C42D3×D414yes—
594C22×C3—22no—
595C22×C3—24no—
596C22×C3—22no—
597C22×C3—24no—
598C22×C3—22no—
599C22×C3—24no—
600C22×C3—41no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3C23×D411yescharacteristic
609C22×C3C23×Q811yescharacteristic
610C22×C3C22×#4111yescharacteristic
611C22×C3C2×H(5,𝔽2)11yescharacteristic
612C22×C3C2×2−1+411yescharacteristic
613C22×C3#58511yescharacteristic
614C22×C3#58511yescharacteristic
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—24no—
618C3×C4—41no—
619C3×C4—42no—
620C3×C4—41no—
621C3×C4—42no—
622C3×C4D4×Q814yes—
623C3×C4#55014yes—
624Dic3—28no—
625Dic3—24no—
626Dic3—42no—
627Dic3—44no—
628Dic3—42no—
629Dic3—42no—
630C23—22no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23C22×Dic614yes—
643C23C22×Dic612yes—
644C23C24×D311yescharacteristic
645Q8—128no—
646Q8—124no—
647Q8—128no—
648D4—28no—
649D4—48no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—28no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—38no—
670C2×C4—34no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—48no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—64no—
677C2×C4—64no—
678C2×C4—62no—
679C2×C4—64no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—64no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—64no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—248no—
691C2×C4C22×Dic612yes—
692C2×C4C22×Dic614yes—
693C2×C4C22×Dic612yes—
694C2×C4C2×D3×D412yes—
695C2×C4C2×D3×D412yes—
696C2×C4C2×D3×D412yes—
697C2×C4#100412yes—
698C2×C4D3×#4112yes—
699C2×C4#101012yes—
700C2×C3—42no—
701C2×C3—44no—
702C2×C3C2×D4×Q811yescharacteristic
703C2×C3C2×#55011yescharacteristic
704C2×C3Q8×#4111yescharacteristic
705C2×C3#348511yescharacteristic
706C2×C3#350111yescharacteristic
707C2×C3#351511yescharacteristic
708C2×C3#354711yescharacteristic
709C22—22no—
710C22—24no—
711C22—24no—
712C22—22no—
713C22—22no—
714C22—24no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—41no—
722C22—42no—
723C22C23×Dic611yescharacteristic
724C22C22×D3×D411yescharacteristic
725C22C2×#100411yescharacteristic
726C22C2×D3×#4111yescharacteristic
727C22C2×#101011yescharacteristic
728C22#596411yescharacteristic
729C22#596411yescharacteristic
730C4—24no—
731C4—22no—
732C4—22no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—68no—
738C4—64no—
739C4—122no—
740C4—122no—
741C4—124no—
742C4—122no—
743C4D4×Dic614yes—
744C4#559914yes—
745C3#5905211yescharacteristic, complemented, Sylow
746C2—42no—
747C2—44no—
748C2C2×D4×Dic611yescharacteristic
749C2#8576611yescharacteristic
750C2#41×Dic611yescharacteristic
751C2C2×#559911yescharacteristic
752C2#8604011yescharacteristic
753C2#8616511yescharacteristic
754C2#8623011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#121C2
prime radicalC2×C3×#121C22
hypercenterC4×#121D3
hypocenterC3#59052
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#121

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#5543C2semidirect
2. C2×#5470C2semidirect
5. #82379C2semidirect
6. #82379C2semidirect
7. #82353C2semidirect
8. C4×#924C2semidirect
9. #76324C2semidirect
10. #76065C2semidirect
11. #75498C2semidirect
12. #74830C2semidirect
13. #73900C2semidirect
14. #73711C2semidirect
15. #73656C2semidirect
16. #73488C2semidirect
17. #73465C2semidirect
113. C3×#121Q8semidirect
174. #869D4semidirect
369. #121Dic6semidirect
745. C3#59052semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#55432
C2×#54702
C3×C4×#1212
#826372
#823792
#823532
C4×#9242
#763242
#760652
#754982
#748302
#739002
#737112
#736562
#734882
#734652
#590523